Lateral stability control of distributed drive electric vehicles via controllable-region analysis and adaptive torque distribution.

Lateral stability of distributed drive electric vehicles (DDEVs) under high-speed and low-adhesion conditions is often evaluated using autonomous phase-plane analysis, which does not explicitly account for closed-loop yaw-moment control and thus yields conservative stability limits. This paper proposes a unified lateral-stability framework that integrates controllable-region (CR) analysis with torque-distribution mode selection under closed-loop control. CRs associated with no control, the differential braking distribution mode (DBDM), and the balanced torque-vectoring distribution mode (BTVDM) are constructed on the sideslip-angle-sideslip-angle-rate phase plane, while control efficiency is assessed in terms of convergence time and execution cost. A gradient-boosted decision-tree ensemble trained on nonlinear vehicle simulations is distilled into a lightweight four-dimensional lookup table for real-time implementation. Results show that, under a representative high-speed and low-adhesion condition (vx=105km/h, μ=0.3), the uncontrolled vehicle fails to satisfy tcmax=3s, whereas DBDM and BTVDM converge within 2.17 s and 2.32 s, respectively. DBDM provides faster recovery near high-risk boundary states, while BTVDM reduces the maximum longitudinal speed loss from 5.96 m/s to 1.40 m/s in closed-loop simulation. The proposed adaptive distribution mode reduces the speed loss by approximately 57.4% compared with pure DBDM, while maintaining comparable peak and RMS sideslip-angle and yaw-rate errors in both simulation and HiL tests.